Results 61 to 70 of about 1,434 (182)

The generalized Kudryashov method for new closed form traveling wave solutions to some NLEEs

AIMS Mathematics, 2019
Dans ce travail, nous construisons des solutions d'ondes progressives de forme fermée pour certaines équations d'évolution non linéaires (NLEE) associées à la physique mathématique. Ce travail met en œuvre la méthode généralisée bien établie de Kudryashov (gKM) pour calculer de nouvelles solutions d'ondes progressives de forme fermée pour l'équation de
Mustafa Habib, Hegagi Mohamed Ali, M. Mamun Miah, M. Ali Akbar   +3 more
openaire   +2 more sources

Dynamical Optical Structure Solutions of the Time‐Fractional Chen‐Lee‐Liu Equation

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
In this article, we utilize the conformable fractional (CF) derivative to investigate the analytically innovative soliton solutions for the time‐fractional nonlinear perturbed Chen‐Lee‐Liu (CLL) equation in optical fibers. An essential governing equation in nonlinear optics, the perturbed CLL model describes the propagation of ultrashort pulses in ...
Shah Muhammad, Abdul Saboor, Muhammad Shakeel, Hameed Gul Ahmadzai, Ivan Giorgio   +4 more
wiley   +1 more source

Dynamical Behavior and Chaotic Nature of M‐Fractional Paraxial Wave Equation With Three Analytical Methods

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid, Mahtab Uddin, Mohammad Safi Ullah, Golam Mostafa, Ashek Ahmed, Shikha Binwal   +5 more
wiley   +1 more source

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

, 2006
The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead ...
Ablowitz M J, Buchberger B, Buchberger B, Conte R, Davenport J, Drouffe J-M, Erdélyi A, Eremenko A E, Fan E, Fan E, Gerdt V P, Ginzburg V L, Hone A N W, Kudryashov N A, Kudryashov N A, Kudryashov N A, Kudryashov N A, Kudryashov N A, Kudryashov N A Demina M V, Landau L D, Nikitin A G Barannyk T A, Porubov A V, S Yu Vernov, Tabor M, Timoshkova E I, Timoshkova E I, Vernov S Yu, Vernov S Yu, Vernov S Yu Ganzha V G Mayr E W Vorozhtsov E V, von Hurwitz A   +29 more
core   +1 more source

Constructing Traveling Wave Solutions via a Generalized Expansion Method for Nonlinear Evolution Equations Possessing Variable Coefficients

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended ...
Abdul Saboor, Xianhua Song, Muhammad Shakeel, Muhammad Qamar Fareed, Baboucarr Ceesay, Kang-Jia Wang   +5 more
wiley   +1 more source

Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches

Journal of Ocean Engineering and Science, 2023
By taking advantage of three different computational analytical methods: the Lie symmetry analysis, the generalized Riccati equation mapping approach, and the modified Kudryashov approach, we construct multiple new analytical soliton solutions to the ...
Shoukry El-Ganaini, Sachin Kumar, Monika Niwas   +2 more
doaj   +1 more source

Construction of Special Solutions for Nonintegrable Systems

, 2006
The Painleve test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist
Ablowitz M J, Antonov V A, Barrow J D, Chang Y F, Chang Y F, Conte R, Conte R, Conte R, Davenport J H, DeWolfe O, Fan E, Golubev V V, Gremm M, Grimshaw R, Hone A N W, Hénon M, Kokubun F, Kowalevski S, Melkonian S, Murray C D, Musette M, Podolský Ji, Porubov A V, Santos G S, Timoshkova E I, Verhoeven C, Verhoeven C, Vernov S Yu, Weiss J, Weiss J, Yomba E   +30 more
core   +1 more source

Dynamics of Computational Solitons: Modulation Instability, Bifurcation, Chaotic Nature With Different Chaos‐Detecting Tools, and Influence of Multiplicative Noise Intensity

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study presents the dynamic analysis of stochastic fractional unstable nonlinear Schrödinger equation (SFuNLSE), focusing on the analysis of bifurcation, chaotic nature, return map, recurrence plots, strange attractor, basin attractor, power spectrum, chaotic nature and also finds the exact optical soliton solution with multiplicative noise ...
Md. Mamunur Roshid, Mohamed Abdalla, M. S. Osman, Smritijit Sen   +3 more
wiley   +1 more source

Simulation of a Combined (2+1)-Dimensional Potential Kadomtsev–Petviashvili Equation via Two Different Methods

Mathematics
This paper presents an investigation into original analytical solutions of the (2+1)-dimensional combined potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations.
Muath Awadalla, Arzu Akbulut, Jihan Alahmadi   +2 more
doaj   +1 more source

Optical Dromion Wave Solutions for the Stochastic Riemann Wave Equation With White Noise Stochastic Term/Random Variable Coefficients and Sensitivity Analysis

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This work introduces a nonlinear stochastic Riemann wave equation (SRWE) with particular novel solutions by using the white noise stochastic term. For the considered problem, we have used two computational methods, namely, the auxiliary equation (AE) method and the unified method (UM), for the exact solution and analyzed their various characteristics ...
Sara Salem Alzaid, Badr Saad T. Alkahtani, Pramita Mishra   +2 more
wiley   +1 more source